Error analysis of eigenvector preprocessors used in adaptive beamforming

Perturbation analysis and Weyl´s inequality are used to determine second order statistics of eigenvalues and eigenvectors of an estimated covariance matrix that arises in an adaptive array processor. An expression for excess mean square error which is caused by the eigenvalue errors is derived. This expression shows that small eigenvalues of the underlying true covariance matrix result in large contributions to the excess mean square error. Closely spaced eigenvalues can cause large errors in eigenvector determination.